Systems and methods for FRC plasma position stability

ABSTRACT

Systems and methods are provided that facilitate stability of an FRC plasma in both radial and axial directions and axial position control of an FRC plasma along the symmetry axis of an FRC plasma chamber. The systems and methods exploit an axially unstable equilibria of the FRC plasma to enforce radial stability, while stabilizing or controlling the axial instability. The systems and methods provide feedback control of the FRC plasma axial position independent of the stability properties of the plasma equilibrium by acting on the voltages applied to a set of external coils concentric with the plasma and using a non-linear control technique.

CROSS-REFERENCE TO RELATED APPLICATIONS

The subject application is a continuation of PCT Patent Application No.PCT/US16/61730, filed Nov. 13, 2016, which claims priority to U.S.Provisional Patent Application No. 62/309,344, filed on Mar. 16, 2016,and U.S. Provisional Patent Application No. 62/255,258, filed on Nov.13, 2015, all of which are incorporated by reference herein in theirentirety for all purposes.

FIELD

The subject matter described herein relates generally to magnetic plasmaconfinement systems having a field reversed configuration (FRC) and,more particularly, to systems and methods that facilitate stability ofan FRC plasma in both radial and axial directions and the control of theFRC plasma position along the symmetry axis of an FRC plasma confinementchamber.

BACKGROUND INFORMATION

The Field Reversed Configuration (FRC) belongs to the class of magneticplasma confinement topologies known as compact toroids (CT). It exhibitspredominantly poloidal magnetic fields and possesses zero or smallself-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033(1988)). The attractions of such a configuration are its simple geometryfor ease of construction and maintenance, a natural unrestricteddivertor for facilitating energy extraction and ash removal, and veryhigh β (β is the ratio of the average plasma pressure to the averagemagnetic field pressure inside the FRC), i.e., high power density. Thehigh β nature is advantageous for economic operation and for the use ofadvanced, aneutronic fuels such as D-He³ and p-B¹¹.

FRC devices are closed, high-vacuum devices relying on a magnetic fieldto confine high-temperature plasmas for, among others, the purpose ofgenerating thermonuclear fusion energy. A component of the magneticfield must necessarily be produced by an intense toroidal current in theplasma, which interacts with the magnetic field produced by externalcoils to the plasma. In contrast with other magnetic confinementdevices, FRC devices have no external coils to produce a toroidal field.A typical FRC plasma resembles an ellipsoid of revolution with its axisalong the external coil axis. The ellipsoid boundary is the plasmaseparatrix, which bounds a compact toroidal plasma with its symmetryaxis along the revolution axis of the ellipsoid.

Due the lack of toroidal magnetic field, FRC plasmas are prone toaxisymmetry breakings that may lead to increased energy, density andconfinement losses if no corrective actions are taken. The most basicinstability relates to the fact that in an FRC plasma the plasma currentflows in opposite direction to the external coil current, whichgenerates a torque which works in the direction to align the plasmacurrent loop with the external field (tilt instability). Otheraxisymmetry breakings relate to the plasma revolution axis shiftingradially (radial shift), an elliptical deformation of the FRC waist(rotational mode) a combination of radial shift and rotation (wobblemode), plasma microturbulence, and others. These axisymmetry breakings,also known as plasma instabilities, must be avoided in order to have agood confinement of the plasma mass and energy.

One of the solutions proposed to achieve stability in the radialdirection is based on the fact that FRC equilibria contains solutions inwhich the plasma position is either stable in the axial direction at theexpense of being unstable in the transverse or radial direction, orstable in the radial direction at the expense of being axially unstable,but not both at the same time. To the first order, an equilibrium wherethe plasma position is transversally stable has the desired property ofbeing axisymmetric, at the expense of being axially unstable. The axialposition instability, however, can be actively controlled using a set ofexternal axisymmetric coils to obtain stability in both axial and radialdirections.

In light of the foregoing, it is, therefore, desirable to providesystems and methods that facilitate the control of the axial position ofan FRC plasma in a way independent of the axial stability properties ofits equilibrium. This is important because the equilibrium may have totransit between an axially stable and unstable equilibria on differentphases of the FRC discharge, for instance if the axial instabilityscenario is temporarily lost and recovered during the plasma discharge.

SUMMARY

The present embodiments provided herein are directed to systems andmethods that facilitate stability of an FRC plasma in both radial andaxial directions and axial position control of an FRC plasma along thesymmetry axis of an FRC plasma confinement chamber independent of theaxial stability properties of the FRC plasma's equilibrium. To the firstorder, an equilibrium where the plasma position is transversally orradially stable has the desired property of being axisymmetric, at theexpense of being axially unstable. The axial position instability,however, is actively controlled using a set of external axisymmetriccoils that control the FRC plasma axial position.

The embodiments presented herein exploit an axially unstable equilibriaof the FRC to enforce radial stability, while stabilizing or controllingthe axial instability. In this way, stability in both axial and radialdirections can be obtained. The control methodology is designed to alterthe external or equilibrium magnetic field to make the FRC plasmaradially or transversally stable at the expense of being axiallyunstable, and then act on the radial field coil current in order toexpeditiously restore the FRC plasma position towards the mid-planewhile minimizing overshooting and/or oscillations around the mid-planeof the confinement chamber. The advantage of this solution is that itreduces the complexity of the actuators required for control. Comparedwith the conventional solutions with multiple degrees of freedom, themethodology of the embodiment presented herein reduces the complexity toa control problem along the FRC plasma revolution axis having one degreeof freedom.

The systems and methods described herein advantageously provide:feedback control of the FRC plasma axial position by acting on thevoltages applied to a set of external coils concentric with the plasma;feedback control of the FRC axial position using a non-linear controltechnique; and, feedback control of the FRC axial position independentlyof the stability properties of the plasma equilibrium. This isindependence is advantageous because the equilibrium may have to transitbetween an axially stable and unstable equilibria on different phases ofthe FRC discharge, for instance if the axial instability scenario istemporarily lost and recovered during the plasma discharge.

The systems, methods, features and advantages of the example embodimentswill be or will become apparent to one with skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional methods, features and advantages beincluded within this description, and be protected by the accompanyingclaims. It is also intended that the claims are not limited to requirethe details of the example embodiments.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawings, which are included as part of the presentspecification, illustrate the presently example embodiments and,together with the general description given above and the detaileddescription of the example embodiments given below, serve to explain andteach the principles of the present invention.

FIG. 1 illustrates particle confinement in the present FRC system undera high performance FRC regime (HPF) versus under a conventional FRCregime (CR), and versus other conventional FRC experiments.

FIG. 2 illustrates the components of the present FRC system and themagnetic topology of an FRC producible in the present FRC system.

FIG. 3A illustrates the basic layout of the present FRC system as viewedfrom the top, including the preferred arrangement of neutral beams,electrodes, plasma guns, mirror plugs and pellet injector.

FIG. 3B illustrates the central confinement vessel as viewed from thetop and showing the neutral beams arranged at an angle normal to themajor axis of symmetry in the central confinement vessel.

FIG. 3C illustrates the central confinement vessel as viewed from thetop and showing the neutral beams arranged at an angle less than normalto the major axis of symmetry in the central confinement vessel anddirected to inject particles toward the mid-plane of the centralconfinement vessel.

FIGS. 3D and 3E illustrate top and perspective views, respectively, ofthe basic layout of an alternative embodiment of the present FRC system,including the preferred arrangement of the central confinement vessel,formation section, inner and outer divertors, neutral beams arranged atan angle less than normal to the major axis of symmetry in the centralconfinement vessel, electrodes, plasma guns and mirror plugs.

FIG. 4 illustrates a schematic of the components of a pulsed powersystem for the formation sections.

FIG. 5 illustrates an isometric view of an individual pulsed powerformation skid.

FIG. 6 illustrates an isometric view of a formation tube assembly.

FIG. 7 illustrates a partial sectional isometric view of neutral beamsystem and key components.

FIG. 8 illustrates an isometric view of the neutral beam arrangement onconfinement chamber.

FIG. 9 illustrates a partial sectional isometric view of a preferredarrangement of the Ti and Li gettering systems.

FIG. 10 illustrates a partial sectional isometric view of a plasma guninstalled in the divertor chamber. Also shown are the associatedmagnetic mirror plug and a divertor electrode assembly.

FIG. 11 illustrates a preferred layout of an annular bias electrode atthe axial end of the confinement chamber.

FIG. 12 illustrates the evolution of the excluded flux radius in the FRCsystem obtained from a series of external diamagnetic loops at the twofield reversed theta pinch formation sections and magnetic probesembedded inside the central metal confinement chamber. Time is measuredfrom the instant of synchronized field reversal in the formationsources, and distance z is given relative to the axial midplane of themachine.

FIGS. 13A, 13B, 13C, and 13D illustrate data from a representativenon-HPF, un-sustained discharge on the present FRC system. Shown asfunctions of time are (FIG. 13A) excluded flux radius at the midplane,(FIG. 13B) 6 chords of line-integrated density from the midplane CO2interferometer, (FIG. 13C) Abel-inverted density radial profiles fromthe CO2 interferometer data, and (FIG. 13D) total plasma temperaturefrom pressure balance.

FIG. 14 illustrates the excluded flux axial profiles at selected timesfor the same discharge of the present FRC system shown in FIGS. 13A,13B, 13C and 13D.

FIG. 15 illustrates an isometric view of the saddle coils mountedoutside of the confinement chamber.

FIGS. 16A, 16B, 16C and 16D illustrate the correlations of FRC lifetimeand pulse length of injected neutral beams. As shown, longer beam pulsesproduce longer lived FRCs.

FIGS. 17A, 17B, 17C and 17D illustrate the individual and combinedeffects of different components of the FRC system on FRC performance andthe attainment of the HPF regime.

FIGS. 18A, 18B, 18C and 18D illustrate data from a representative HPF,un-sustained discharge on the present FRC system. Shown as functions oftime are (FIG. 18A) excluded flux radius at the midplane, (FIG. 18B) 6chords of line-integrated density from the midplane CO2 interferometer,(FIG. 18C) Abel-inverted density radial profiles from the CO2interferometer data, and (FIG. 18D) total plasma temperature frompressure balance.

FIG. 19 illustrates flux confinement as a function of electrontemperature (T_(e)). It represents a graphical representation of a newlyestablished superior scaling regime for HPF discharges.

FIG. 20 illustrates the FRC lifetime corresponding to the pulse lengthof non-angled and angled injected neutral beams.

FIGS. 21A and 21B illustrate the basic layout of a compact toroid (CT)injector.

FIGS. 22A and 22B illustrate the central confinement vessel showing theCT injector mounted thereto.

FIGS. 23A and 23B illustrate the basic layout of an alternativeembodiment of the CT injector having a drift tube coupled thereto.

FIG. 24 is a schematic of illustrating an axial position controlmechanism of an FRC plasma within a confining vessel (CV).

FIG. 25 is a flow diagram of a generic sliding mode control scheme.

FIG. 26 is a composite graph of examples of a sliding mode axialposition control simulation.

FIG. 27 is a composite graph of examples of a sliding mode axialposition control simulation.

It should be noted that the figures are not necessarily drawn to scaleand that elements of similar structures or functions are generallyrepresented by like reference numerals for illustrative purposesthroughout the figures. It also should be noted that the figures areonly intended to facilitate the description of the various embodimentsdescribed herein. The figures do not necessarily describe every aspectof the teachings disclosed herein and do not limit the scope of theclaims.

DETAILED DESCRIPTION

The present embodiments provided herein are directed to systems andmethods that facilitate stability of an FRC plasma in both radial andaxial directions and axial position control of an FRC plasma along thesymmetry axis of an FRC plasma confinement chamber independent of theaxial stability properties of the FRC plasma's equilibrium.Representative examples of the embodiments described herein, whichexamples utilize many of these additional features and teachings bothseparately and in combination, will now be described in further detailwith reference to the attached drawings. This detailed description ismerely intended to teach a person of skill in the art further detailsfor practicing preferred aspects of the present teachings and is notintended to limit the scope of the invention. Therefore, combinations offeatures and steps disclosed in the following detail description may notbe necessary to practice the invention in the broadest sense, and areinstead taught merely to particularly describe representative examplesof the present teachings.

Moreover, the various features of the representative examples and thedependent claims may be combined in ways that are not specifically andexplicitly enumerated in order to provide additional useful embodimentsof the present teachings. In addition, it is expressly noted that allfeatures disclosed in the description and/or the claims are intended tobe disclosed separately and independently from each other for thepurpose of original disclosure, as well as for the purpose ofrestricting the claimed subject matter independent of the compositionsof the features in the embodiments and/or the claims. It is alsoexpressly noted that all value ranges or indications of groups ofentities disclose every possible intermediate value or intermediateentity for the purpose of original disclosure, as well as for thepurpose of restricting the claimed subject matter.

Conventional solutions to FRC instabilities typically provide stabilityin the axial direction at the expense of being unstable in the radialdirection, or stability in the radial direction at the expense of beingaxially unstable, but not stability in both directions at the same time.To the first order, an equilibrium where the plasma position istransversally or radially stable has the desired property of beingaxisymmetric, at the expense of being axially unstable. In view of theforegoing, the embodiments provided herein are directed to systems andmethods that facilitate stability of an FRC plasma in both radial andaxial directions and axial position control of an FRC plasma along thesymmetry axis of an FRC plasma confinement chamber independent of theaxial stability properties of the FRC plasma's equilibrium. The axialposition instability, however, is actively controlled using a set ofexternal axisymmetric coils that control the FRC plasma axial position.The systems and methods provide feedback control of the FRC plasma axialposition independent of the stability properties of the plasmaequilibrium by acting on the voltages applied to a set of external coilsconcentric with the plasma and using a non-linear control technique.

The embodiments presented herein exploit an axially unstable equilibriaof the FRC to enforce radial stability, while stabilizing or controllingthe axial instability. In this way, stability in both axial and radialdirections can be obtained. The control methodology is designed to alterthe external or equilibrium magnetic field to make the FRC plasmaradially or transversally stable at the expense of being axiallyunstable, and then act on the radial field coil current in order toexpeditiously restore the FRC plasma position towards the mid-planewhile minimizing overshooting and/or oscillations around the mid-planeof the confinement chamber. The advantage of this solution is that itreduces the complexity of the actuators required for control. Comparedwith the conventional solutions with multiple degrees of freedom, themethodology of the embodiment presented herein reduces the complexity toa control problem along the FRC plasma revolution axis having one degreeof freedom.

The combination of waveforms in coil currents, fueling and neutral beampower that result into an axially unstable plasma define the plasmacontrol scenario that sets the plasma into an axial unstable situation.The scenario can be pre-programmed using prior knowledge of simulationsor experiments, or feedback controlled to maintain an equilibrium thatis axially unstable. The plasma position should be controlled during thedischarges independently of the stability properties of the equilibrium,e.g. the control scheme should work for either axially stable or axiallyunstable plasmas, up to a limit. The most axially unstable plasma thatcan be controlled has a growth time comparable to the skin time of thevessel.

Before turning to the systems and methods that facilitate stability ofan FRC plasma in both radial and axial directions and axial positioncontrol of an FRC plasma along the symmetry axis of an FRC plasmaconfinement chamber, a discussion of systems and methods for forming andmaintaining high performance FRCs with superior stability as well assuperior particle, energy and flux confinement over conventional FRCs isprovided. Such high performance FRCs provide a pathway to a wholevariety of applications including compact neutron sources (for medicalisotope production, nuclear waste remediation, materials research,neutron radiography and tomography), compact photon sources (forchemical production and processing), mass separation and enrichmentsystems, and reactor cores for fusion of light nuclei for the futuregeneration of energy.

Various ancillary systems and operating modes have been explored toassess whether there is a superior confinement regime in FRCs. Theseefforts have led to breakthrough discoveries and the development of aHigh Performance FRC paradigm described herein. In accordance with thisnew paradigm, the present systems and methods combine a host of novelideas and means to dramatically improve FRC confinement as illustratedin FIG. 1 as well as provide stability control without negativeside-effects. As discussed in greater detail below, FIG. 1 depictsparticle confinement in an FRC system 10 described below (see FIGS. 2and 3), operating in accordance with a High Performance FRC regime (HPF)for forming and maintaining an FRC versus operating in accordance with aconventional regime CR for forming and maintaining an FRC, and versusparticle confinement in accordance with conventional regimes for formingand maintaining an FRC used in other experiments. The present disclosurewill outline and detail the innovative individual components of the FRCsystem 10 and methods as well as their collective effects.

FRC System

Vacuum System

FIGS. 2 and 3A depict a schematic of the present FRC system 10. The FRCsystem 10 includes a central confinement vessel 100 surrounded by twodiametrically opposed reversed-field-theta-pinch formation sections 200and, beyond the formation sections 200, two divertor chambers 300 tocontrol neutral density and impurity contamination. The present FRCsystem 10 was built to accommodate ultrahigh vacuum and operates attypical base pressures of 10⁻⁸ torr. Such vacuum pressures require theuse of double-pumped mating flanges between mating components, metalO-rings, high purity interior walls, as well as careful initial surfaceconditioning of all parts prior to assembly, such as physical andchemical cleaning followed by a 24 hour 250° C. vacuum baking andHydrogen glow discharge cleaning.

The reversed-field-theta-pinch formation sections 200 are standardfield-reversed-theta-pinches (FRTPs), albeit with an advanced pulsedpower formation system discussed in detail below (see FIGS. 4 through6). Each formation section 200 is made of standard opaque industrialgrade quartz tubes that feature a 2 millimeter inner lining of ultrapurequartz. The confinement chamber 100 is made of stainless steel to allowa multitude of radial and tangential ports; it also serves as a fluxconserver on the timescale of the experiments described below and limitsfast magnetic transients. Vacuums are created and maintained within theFRC system 10 with a set of dry scroll roughing pumps, turbo molecularpumps and cryo pumps.

Magnetic System

The magnetic system 400 is illustrated in FIGS. 2 and 3A. FIG. 2,amongst other features, illustrates an FRC magnetic flux and densitycontours (as functions of the radial and axial coordinates) pertainingto an FRC 450 producible by the FRC system 10. These contours wereobtained by a 2-D resistive Hall-MHD numerical simulation using codedeveloped to simulate systems and methods corresponding to the FRCsystem 10, and agree well with measured experimental data. As seen inFIG. 2, the FRC 450 consists of a torus of closed field lines at theinterior 453 of the FRC 450 inside a separatrix 451, and of an annularedge layer 456 on the open field lines 452 just outside the separatrix451. The edge layer 456 coalesces into jets 454 beyond the FRC length,providing a natural divertor.

The main magnetic system 410 includes a series of quasi-dc coils 412,414, and 416 that are situated at particular axial positions along thecomponents, i.e., along the confinement chamber 100, the formationsections 200 and the divertors 300, of the FRC system 10. The quasi-dccoils 412, 414 and 416 are fed by quasi-dc switching power supplies andproduce basic magnetic bias fields of about 0.1 T in the confinementchamber 100, the formation sections 200 and the divertors 300. Inaddition to the quasi-dc coils 412, 414 and 416, the main magneticsystem 410 includes quasi-dc mirror coils 420 (fed by switchingsupplies) between either end of the confinement chamber 100 and theadjacent formation sections 200. The quasi-dc mirror coils 420 providemagnetic mirror ratios of up to 5 and can be independently energized forequilibrium shaping control. In addition, mirror plugs 440, arepositioned between each of the formation sections 200 and divertors 300.The mirror plugs 440 comprise compact quasi-dc mirror coils 430 andmirror plug coils 444. The quasi-dc mirror coils 430 include three coils432, 434 and 436 (fed by switching supplies) that produce additionalguide fields to focus the magnetic flux surfaces 455 towards the smalldiameter passage 442 passing through the mirror plug coils 444. Themirror plug coils 444, which wrap around the small diameter passage 442and are fed by LC pulsed power circuitry, produce strong magnetic mirrorfields of up to 4 T. The purpose of this entire coil arrangement is totightly bundle and guide the magnetic flux surfaces 455 andend-streaming plasma jets 454 into the remote chambers 310 of thedivertors 300. Finally, a set of saddle-coil “antennas” 460 (see FIG.15) are located outside the confinement chamber 100, two on each side ofthe mid-plane, and are fed by dc power supplies. The saddle-coilantennas 460 can be configured to provide a quasi-static magnetic dipoleor quadrupole field of about 0.01 T for controlling rotationalinstabilities and/or electron current control. The saddle-coil antennas460 can flexibly provide magnetic fields that are either symmetric orantisymmetric about the machine's midplane, depending on the directionof the applied currents.

Pulsed Power Formation Systems

The pulsed power formation systems 210 operate on a modified theta-pinchprinciple. There are two systems that each power one of the formationsections 200. FIGS. 4 through 6 illustrate the main building blocks andarrangement of the formation systems 210. The formation system 210 iscomposed of a modular pulsed power arrangement that consists ofindividual units (=skids) 220 that each energize a sub-set of coils 232of a strap assembly 230 (=straps) that wrap around the formation quartztubes 240. Each skid 220 is composed of capacitors 221, inductors 223,fast high current switches 225 and associated trigger 222 and dumpcircuitry 224. In total, each formation system 210 stores between350-400 kJ of capacitive energy, which provides up to 35 GW of power toform and accelerate the FRCs. Coordinated operation of these componentsis achieved via a state-of-the-art trigger and control system 222 and224 that allows synchronized timing between the formation systems 210 oneach formation section 200 and minimizes switching jitter to tens ofnanoseconds. The advantage of this modular design is its flexibleoperation: FRCs can be formed in-situ and then accelerated and injected(=static formation) or formed and accelerated at the same time (=dynamicformation).

Neutral Beam Injectors

Neutral atom beams 600 are deployed on the FRC system 10 to provideheating and current drive as well as to develop fast particle pressure.As shown in FIGS. 3A, 3B and 8, the individual beam lines comprisingneutral atom beam injector systems 610 and 640 are located around thecentral confinement chamber 100 and inject fast particles tangentiallyto the FRC plasma (and perpendicular or at an angel normal to the majoraxis of symmetry in the central confinement vessel 100) with an impactparameter such that the target trapping zone lies well within theseparatrix 451 (see FIG. 2). Each injector system 610 and 640 is capableof injecting up to 1 MW of neutral beam power into the FRC plasma withparticle energies between 20 and 40 keV. The systems 610 and 640 arebased on positive ion multi-aperture extraction sources and utilizegeometric focusing, inertial cooling of the ion extraction grids anddifferential pumping. Apart from using different plasma sources, thesystems 610 and 640 are primarily differentiated by their physicaldesign to meet their respective mounting locations, yielding side andtop injection capabilities. Typical components of these neutral beaminjectors are specifically illustrated in FIG. 7 for the side injectorsystems 610. As shown in FIG. 7, each individual neutral beam system 610includes an RF plasma source 612 at an input end (this is substitutedwith an arc source in systems 640) with a magnetic screen 614 coveringthe end. An ion optical source and acceleration grids 616 is coupled tothe plasma source 612 and a gate valve 620 is positioned between the ionoptical source and acceleration grids 616 and a neutralizer 622. Adeflection magnet 624 and an ion dump 628 are located between theneutralizer 622 and an aiming device 630 at the exit end. A coolingsystem comprises two cryo-refrigerators 634, two cryopanels 636 and aLN2 shroud 638. This flexible design allows for operation over a broadrange of FRC parameters.

An alternative configuration for the neutral atom beam injectors 600 isthat of injecting the fast particles tangentially to the FRC plasma, butwith an angle A less than 90° relative to the major axis of symmetry inthe central confinement vessel 100. These types of orientation of thebeam injectors 615 are shown in FIGS. 3C, 3D and 3E. In addition, thebeam injectors 615 may be oriented such that the beam injectors 615 oneither side of the mid-plane of the central confinement vessel 100inject their particles towards the mid-plane. Finally, the axialposition of these beam systems 600 may be chosen closer to themid-plane. These alternative injection embodiments facilitate a morecentral fueling option, which provides for better coupling of the beamsand higher trapping efficiency of the injected fast particles.Furthermore, depending on the angle and axial position, this arrangementof the beam injectors 615 allows more direct and independent control ofthe axial elongation and other characteristics of the FRC 450. Forinstance, injecting the beams at a shallow angle A relative to thevessel's major axis of symmetry will create an FRC plasma with longeraxial extension and lower temperature while picking a more perpendicularangle A will lead to an axially shorter but hotter plasma. In thisfashion the injection angle A and location of the beam injectors 615 canbe optimized for different purposes. In addition, such angling andpositioning of the beam injectors 615 can allow beams of higher energy(which is generally more favorable for depositing more power with lessbeam divergence) to be injected into lower magnetic fields than wouldotherwise be necessary to trap such beams. This is due to the fact thatit is the azimuthal component of the energy that determines fast ionorbit scale (which becomes progressively smaller as the injection anglerelative to the vessel's major axis of symmetry is reduced at constantbeam energy). Furthermore, angled injection towards the mid-plane andwith axial beam positions close to the mid-plane improves beam-plasmacoupling, even as the FRC plasma shrinks or otherwise axially contractsduring the injection period.

Turning to FIGS. 3D and 3E, another alternative configuration includesinner divertors 302 in addition to the angled beam injectors 615. Theinner divertors 302 are positioned between the formation sections 200and the confinement chamber 100, and are configured and operatesubstantially similar to the outer divertors 300. The inner divertors302, which include fast switching magnetic coils therein, areeffectively inactive during the formation process to enable theformation FRCs to pass through the inner divertors 302 as the formationFRCs translate toward the mid-plane of the confinement chamber 100. Oncethe formation FRCs pass through the inner divertors 302 into theconfinement chamber 100, the inner divertors are activated to operatesubstantially similar to the outer divertors and isolate the confinementchamber 100 from the formation sections 200.

Pellet Injector

To provide a means to inject new particles and better control FRCparticle inventory, a 12-barrel pellet injector 700 (see e.g. I. Vinyaret al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,”Proceedings of the 26th Fusion Science and Technology Symposium, 09/27to 10/01 (2010)) is utilized on FRC system 10. FIG. 3A illustrates thelayout of the pellet injector 700 on the FRC system 10. The cylindricalpellets (D˜1 mm, L˜1-2 mm) are injected into the FRC with a velocity inthe range of 150-250 km/s. Each individual pellet contains about 5×10¹⁹hydrogen atoms, which is comparable to the FRC particle inventory.

Gettering Systems

It is well known that neutral halo gas is a serious problem in allconfinement systems. The charge exchange and recycling (release of coldimpurity material from the wall) processes can have a devastating effecton energy and particle confinement. In addition, any significant densityof neutral gas at or near the edge will lead to prompt losses of or atleast severely curtail the lifetime of injected large orbit (highenergy) particles (large orbit refers to particles having orbits on thescale of the FRC topology or at least orbit radii much larger than thecharacteristic magnetic field gradient length scale)—a fact that isdetrimental to all energetic plasma applications, including fusion viaauxiliary beam heating.

Surface conditioning is a means by which the detrimental effects ofneutral gas and impurities can be controlled or reduced in a confinementsystem. To this end the FRC system 10 provided herein employs Titaniumand Lithium deposition systems 810 and 820 that coat the plasma facingsurfaces of the confinement chamber (or vessel) 100 and diverters 300and 302 with films (tens of micrometers thick) of Ti and/or Li. Thecoatings are achieved via vapor deposition techniques. Solid Li and/orTi are evaporated and/or sublimated and sprayed onto nearby surfaces toform the coatings. The sources are atomic ovens with guide nozzles (incase of Li) 822 or heated spheres of solid with guide shrouding (in caseof Ti) 812. Li evaporator systems typically operate in a continuous modewhile Ti sublimators are mostly operated intermittently in betweenplasma operation. Operating temperatures of these systems are above 600°C. to obtain fast deposition rates. To achieve good wall coverage,multiple strategically located evaporator/sublimator systems arenecessary. FIG. 9 details a preferred arrangement of the getteringdeposition systems 810 and 820 in the FRC system 10. The coatings act asgettering surfaces and effectively pump atomic and molecular hydrogenicspecies (H and D). The coatings also reduce other typical impuritiessuch as Carbon and Oxygen to insignificant levels.

Mirror Plugs

As stated above, the FRC system 10 employs sets of mirror coils 420,430, and 444 as shown in FIGS. 2 and 3A. A first set of mirror coils 420is located at the two axial ends of the confinement chamber 100 and isindependently energized from the confinement coils 412, 414 and 416 ofthe main magnetic system 410. The first set of mirror coils 420primarily helps to steer and axially contain the FRC 450 during mergingand provides equilibrium shaping control during sustainment. The firstmirror coil set 420 produces nominally higher magnetic fields (around0.4 to 0.5 T) than the central confinement field produced by the centralconfinement coils 412. The second set of mirror coils 430, whichincludes three compact quasi-dc mirror coils 432, 434 and 436, islocated between the formation sections 200 and the divertors 300 and aredriven by a common switching power supply. The mirror coils 432, 434 and436, together with the more compact pulsed mirror plug coils 444 (fed bya capacitive power supply) and the physical constriction 442 form themirror plugs 440 that provide a narrow low gas conductance path withvery high magnetic fields (between 2 to 4 T with rise times of about 10to 20 ms). The most compact pulsed mirror coils 444 are of compactradial dimensions, bore of 20 cm and similar length, compared to themeter-plus-scale bore and pancake design of the confinement coils 412,414 and 416. The purpose of the mirror plugs 440 is multifold: (1) Thecoils 432, 434, 436 and 444 tightly bundle and guide the magnetic fluxsurfaces 452 and end-streaming plasma jets 454 into the remote divertorchambers 300. This assures that the exhaust particles reach thedivertors 300 appropriately and that there are continuous flux surfaces455 that trace from the open field line 452 region of the central FRC450 all the way to the divertors 300. (2) The physical constrictions 442in the FRC system 10, through which that the coils 432, 434, 436 and 444enable passage of the magnetic flux surfaces 452 and plasma jets 454,provide an impediment to neutral gas flow from the plasma guns 350 thatsit in the divertors 300. In the same vein, the constrictions 442prevent back-streaming of gas from the formation sections 200 to thedivertors 300 thereby reducing the number of neutral particles that hasto be introduced into the entire FRC system 10 when commencing thestartup of an FRC. (3) The strong axial mirrors produced by the coils432, 434, 436 and 444 reduce axial particle losses and thereby reducethe parallel particle diffusivity on open field lines.

In the alternative configuration shown in FIGS. 3D and 3E, a set of lowprofile necking coils 421 are positions between the inner divertors 302and the formations sections 200.

Axial Plasma Guns

Plasma streams from guns 350 mounted in the divertor chambers 310 of thedivertors 300 are intended to improve stability and neutral beamperformance. The guns 350 are mounted on axis inside the chamber 310 ofthe divertors 300 as illustrated in FIGS. 3D and 10 and produce plasmaflowing along the open flux lines 452 in the divertor 300 and towardsthe center of the confinement chamber 100. The guns 350 operate at ahigh density gas discharge in a washer-stack channel and are designed togenerate several kiloamperes of fully ionized plasma for 5 to 10 ms. Theguns 350 include a pulsed magnetic coil that matches the output plasmastream with the desired size of the plasma in the confinement chamber100. The technical parameters of the guns 350 are characterized by achannel having a 5 to 13 cm outer diameter and up to about 10 cm innerdiameter and provide a discharge current of 10-15 kA at 400-600 V with agun-internal magnetic field of between 0.5 to 2.3 T.

The gun plasma streams can penetrate the magnetic fields of the mirrorplugs 440 and flow into the formation section 200 and confinementchamber 100. The efficiency of plasma transfer through the mirror plug440 increases with decreasing distance between the gun 350 and the plug440 and by making the plug 440 wider and shorter. Under reasonableconditions, the guns 350 can each deliver approximately 10²² protons/sthrough the 2 to 4 T mirror plugs 440 with high ion and electrontemperatures of about 150 to 300 eV and about 40 to 50 eV, respectively.The guns 350 provide significant refueling of the FRC edge layer 456,and an improved overall FRC particle confinement.

To further increase the plasma density, a gas box could be utilized topuff additional gas into the plasma stream from the guns 350. Thistechnique allows a several-fold increase in the injected plasma density.In the FRC system 10, a gas box installed on the divertor 300 side ofthe mirror plugs 440 improves the refueling of the FRC edge layer 456,formation of the FRC 450, and plasma line-tying.

Given all the adjustment parameters discussed above and also taking intoaccount that operation with just one or both guns is possible, it isreadily apparent that a wide spectrum of operating modes is accessible.

Biasing Electrodes

Electrical biasing of open flux surfaces can provide radial potentialsthat give rise to azimuthal EXB motion that provides a controlmechanism, analogous to turning a knob, to control rotation of the openfield line plasma as well as the actual FRC core 450 via velocity shear.To accomplish this control, the FRC system 10 employs various electrodesstrategically placed in various parts of the machine. FIGS. 3A and 3Ddepicts biasing electrodes positioned at preferred locations within theFRC system 10.

In principle, there are 4 classes of electrodes: (1) point electrodes905 in the confinement chamber 100 that make contact with particularopen field lines 452 in the edge of the FRC 450 to provide localcharging, (2) annular electrodes 900 between the confinement chamber 100and the formation sections 200 to charge far-edge flux layers 456 in anazimuthally symmetric fashion, (3) stacks of concentric electrodes 910in the divertors 300 to charge multiple concentric flux layers 455(whereby the selection of layers is controllable by adjusting coils 416to adjust the divertor magnetic field so as to terminate the desiredflux layers 456 on the appropriate electrodes 910), and finally (4) theanodes 920 (see FIG. 10) of the plasma guns 350 themselves (whichintercept inner open flux surfaces 455 near the separatrix of the FRC450). FIGS. 10 and 11 show some typical designs for some of these.

In all cases these electrodes are driven by pulsed or dc power sourcesat voltages up to about 800 V. Depending on electrode size and what fluxsurfaces are intersected, currents can be drawn in the kilo-ampererange.

Un-Sustained Operation of FRC System—Conventional Regime

The standard plasma formation on the FRC system 10 follows thewell-developed reversed-field-theta-pinch technique. A typical processfor starting up an FRC commences by driving the quasi-dc coils 412, 414,416, 420, 432, 434 and 436 to steady state operation. The RFTP pulsedpower circuits of the pulsed power formation systems 210 then drive thepulsed fast reversed magnet field coils 232 to create a temporaryreversed bias of about −0.05 T in the formation sections 200. At thispoint a predetermined amount of neutral gas at 9-20 psi is injected intothe two formation volumes defined by the quartz-tube chambers 240 of the(north and south) formation sections 200 via a set ofazimuthally-oriented puff-vales at flanges located on the outer ends ofthe formation sections 200. Next a small RF (˜hundreds of kilo-hertz)field is generated from a set of antennas on the surface of the quartztubes 240 to create pre-ionization in the form of local seed ionizationregions within the neutral gas columns. This is followed by applying atheta-ringing modulation on the current driving the pulsed fast reversedmagnet field coils 232, which leads to more global pre-ionization of thegas columns. Finally, the main pulsed power banks of the pulsed powerformation systems 210 are fired to drive pulsed fast reversed magnetfield coils 232 to create a forward-biased field of up to 0.4 T. Thisstep can be time-sequenced such that the forward-biased field isgenerated uniformly throughout the length of the formation tubes 240(static formation) or such that a consecutive peristaltic fieldmodulation is achieved along the axis of the formation tubes 240(dynamic formation).

In this entire formation process, the actual field reversal in theplasma occurs rapidly, within about 5 μs. The multi-gigawatt pulsedpower delivered to the forming plasma readily produces hot FRCs whichare then ejected from the formation sections 200 via application ofeither a time-sequenced modulation of the forward magnetic field(magnetic peristalsis) or temporarily increased currents in the lastcoils of coil sets 232 near the axial outer ends of the formation tubes210 (forming an axial magnetic field gradient that points axiallytowards the confinement chamber 100). The two (north and south)formation FRCs so formed and accelerated then expand into the largerdiameter confinement chamber 100, where the quasi-dc coils 412 produce aforward-biased field to control radial expansion and provide theequilibrium external magnetic flux.

Once the north and south formation FRCs arrive near the midplane of theconfinement chamber 100, the FRCs collide. During the collision theaxial kinetic energies of the north and south formation FRCs are largelythermalized as the FRCs merge ultimately into a single FRC 450. A largeset of plasma diagnostics are available in the confinement chamber 100to study the equilibria of the FRC 450. Typical operating conditions inthe FRC system 10 produce compound FRCs with separatrix radii of about0.4 m and about 3 m axial extend. Further characteristics are externalmagnetic fields of about 0.1 T, plasma densities around 5×10¹⁹ m⁻³ andtotal plasma temperature of up to 1 keV. Without any sustainment, i.e.,no heating and/or current drive via neutral beam injection or otherauxiliary means, the lifetime of these FRCs is limited to about 1 ms,the indigenous characteristic configuration decay time.

Experimental Data of Unsustained Operation—Conventional Regime

FIG. 12 shows a typical time evolution of the excluded flux radius,r_(ΔΦ), which approximates the separatrix radius, r_(s), to illustratethe dynamics of the theta-pinch merging process of the FRC 450. The two(north and south) individual plasmoids are produced simultaneously andthen accelerated out of the respective formation sections 200 at asupersonic speed, v_(Z)˜250 km/s, and collide near the midplane at z=0.During the collision the plasmoids compress axially, followed by a rapidradial and axial expansion, before eventually merging to form an FRC450. Both radial and axial dynamics of the merging FRC 450 are evidencedby detailed density profile measurements and bolometer-based tomography.

Data from a representative un-sustained discharge of the FRC system 10are shown as functions of time in FIGS. 13A, 13B, 13C, and 13D. The FRCis initiated at t=0. The excluded flux radius at the machine's axialmid-plane is shown in FIG. 13A. This data is obtained from an array ofmagnetic probes, located just inside the confinement chamber's stainlesssteel wall, that measure the axial magnetic field. The steel wall is agood flux conserver on the time scales of this discharge.

Line-integrated densities are shown in FIG. 13B, from a 6-chordCO₂/He—Ne interferometer located at z=0. Taking into account vertical(y) FRC displacement, as measured by bolometric tomography, Abelinversion yields the density contours of FIG. 13C. After some axial andradial sloshing during the first 0.1 ms, the FRC settles with a hollowdensity profile. This profile is fairly flat, with substantial densityon axis, as required by typical 2-D FRC equilibria.

Total plasma temperature is shown in FIG. 13D, derived from pressurebalance and fully consistent with Thomson scattering and spectroscopymeasurements.

Analysis from the entire excluded flux array indicates that the shape ofthe FRC separatrix (approximated by the excluded flux axial profiles)evolves gradually from racetrack to elliptical. This evolution, shown inFIG. 14, is consistent with a gradual magnetic reconnection from two toa single FRC. Indeed, rough estimates suggest that in this particularinstant about 10% of the two initial FRC magnetic fluxes reconnectsduring the collision.

The FRC length shrinks steadily from 3 down to about 1 m during the FRClifetime. This shrinkage, visible in FIG. 14, suggests that mostlyconvective energy loss dominates the FRC confinement. As the plasmapressure inside the separatrix decreases faster than the externalmagnetic pressure, the magnetic field line tension in the end regionscompresses the FRC axially, restoring axial and radial equilibrium. Forthe discharge discussed in FIGS. 13A, 13B, 13C, 13D and 14, the FRCmagnetic flux, particle inventory, and thermal energy (about 10 mWb,7×10¹⁹ particles, and 7 kJ, respectively) decrease by roughly an orderof magnitude in the first millisecond, when the FRC equilibrium appearsto subside.

Sustained Operation—HPF Regime

The examples in FIGS. 12 to 14 are characteristic of decaying FRCswithout any sustainment. However, several techniques are deployed on theFRC system 10 to further improve FRC confinement (inner core and edgelayer) to the HPF regime and sustain the configuration.

Neutral Beams

First, fast (H) neutrals are injected perpendicular to B_(z) in beamsfrom the eight neutral beam injectors 600. The beams of fast neutralsare injected from the moment the north and south formation FRCs merge inthe confinement chamber 100 into one FRC 450. The fast ions, createdprimarily by charge exchange, have betatron orbits (with primary radiion the scale of the FRC topology or at least much larger than thecharacteristic magnetic field gradient length scale) that add to theazimuthal current of the FRC 450. After some fraction of the discharge(after 0.5 to 0.8 ms into the shot), a sufficiently large fast ionpopulation significantly improves the inner FRC's stability andconfinement properties (see e.g. MW. Binderbauer and N. Rostoker, PlasmaPhys. 56, part 3, 451 (1996)). Furthermore, from a sustainmentperspective, the beams from the neutral beam injectors 600 are also theprimary means to drive current and heat the FRC plasma.

In the plasma regime of the FRC system 10, the fast ions slow downprimarily on plasma electrons. During the early part of a discharge,typical orbit-averaged slowing-down times of fast ions are 0.3-0.5 ms,which results in significant FRC heating, primarily of electrons. Thefast ions make large radial excursions outside of the separatrix becausethe internal FRC magnetic field is inherently low (about 0.03 T onaverage for a 0.1 T external axial field). The fast ions would bevulnerable to charge exchange loss, if the neutral gas density were toohigh outside of the separatrix. Therefore, wall gettering and othertechniques (such as the plasma gun 350 and mirror plugs 440 thatcontribute, amongst other things, to gas control) deployed on the FRCsystem 10 tend to minimize edge neutrals and enable the requiredbuild-up of fast ion current.

Pellet Injection

When a significant fast ion population is built up within the FRC 450,with higher electron temperatures and longer FRC lifetimes, frozen H orD pellets are injected into the FRC 450 from the pellet injector 700 tosustain the FRC particle inventory of the FRC 450. The anticipatedablation timescales are sufficiently short to provide a significant FRCparticle source. This rate can also be increased by enlarging thesurface area of the injected piece by breaking the individual pelletinto smaller fragments while in the barrels or injection tubes of thepellet injector 700 and before entering the confinement chamber 100, astep that can be achieved by increasing the friction between the pelletand the walls of the injection tube by tightening the bend radius of thelast segment of the injection tube right before entry into theconfinement chamber 100. By virtue of varying the firing sequence andrate of the 12 barrels (injection tubes) as well as the fragmentation,it is possible to tune the pellet injection system 700 to provide justthe desired level of particle inventory sustainment. In turn, this helpsmaintain the internal kinetic pressure in the FRC 450 and sustainedoperation and lifetime of the FRC 450.

Once the ablated atoms encounter significant plasma in the FRC 450, theybecome fully ionized. The resultant cold plasma component is thencollisionally heated by the indigenous FRC plasma. The energy necessaryto maintain a desired FRC temperature is ultimately supplied by the beaminjectors 600. In this sense the pellet injectors 700 together with theneutral beam injectors 600 form the system that maintains a steady stateand sustains the FRC 450.

CT Injector

As an alternative to the pellet injector, a compact toroid (CT) injectoris provided, mainly for fueling field-reversed configuration (FRCs)plasmas. The CT injector 720 comprises a magnetized coaxial plasma-gun(MCPG), which, as shown in FIGS. 21A and 21B, includes coaxialcylindrical inner and outer electrodes 722 and 724, a bias coilpositioned internal to the inner electrode 726 and an electrical break728 on an end opposite the discharge of the CT injector 720. Gas isinjected through a gas injection port 730 into a space between the innerand outer electrodes 722 and 724 and a Spheromak-like plasma isgenerated therefrom by discharge and pushed out from the gun by Lorentzforce. As shown in FIGS. 22A and 22B, a pair of CT injectors 720 arecoupled to the confinement vessel 100 near and on opposition sides ofthe mid-plane of the vessel 100 to inject CTs into the central FRCplasma within the confinement vessel 100. The discharge end of the CTinjectors 720 are directed towards the mid-plane of the confinementvessel 100 at an angel to the longitudinal axis of the confinementvessel 100 similar to the neutral beam injectors 615.

In an alternative embodiments, the CT injector 720, as shown in FIGS.23A and 23B, include a drift tube 740 comprising an elongate cylindricaltube coupled to the discharge end of the CT injector 720. As depicted,the drift tube 740 includes drift tube coils 742 positioned about andaxially spaced along the tube. A plurality of diagnostic ports 744 aredepicted along the length of the tube.

The advantages of the CT injector 720 are: (1) control and adjustabilityof particle inventory per injected CT; (2) warm plasma is deposited(instead of cryogenic pellets); (3) system can be operated in rep-ratemode so as to allow for continuous fueling; (4) the system can alsorestore some magnetic flux as the injected CTs carry embedded magneticfield. In an embodiment for experimental use, the inner diameter of anouter electrode is 83.1 mm and the outer diameter of an inner electrodeis 54.0 mm. The surface of the inner electrode 722 is preferably coatedwith tungsten in order to reduce impurities coming out from theelectrode 722. As depicted, the bias coil 726 is mounted inside of theinner electrode 722.

In recent experiments a supersonic CT translation speed of up to ˜100km/s was achieved. Other typical plasma parameters are as follows:electron density ˜5×1021 m−3, electron temperature ˜30-50 eV, andparticle inventory of ˜0.5-1.0×1019. The high kinetic pressure of the CTallows the injected plasma to penetrate deeply into the FRC and depositthe particles inside the separatrix. In recent experiments FRC particlefueling has resulted in ˜10-20% of the FRC particle inventory beingprovide by the CT injectors successfully demonstrating fueling canreadily be carried out without disrupting the FRC plasma.

Saddle Coils

To achieve steady state current drive and maintain the required ioncurrent it is desirable to prevent or significantly reduce electron spinup due to the electron-ion frictional force (resulting from collisionalion electron momentum transfer). The FRC system 10 utilizes aninnovative technique to provide electron breaking via an externallyapplied static magnetic dipole or quadrupole field. This is accomplishedvia the external saddle coils 460 depicted in FIG. 15. The transverseapplied radial magnetic field from the saddle coils 460 induces an axialelectric field in the rotating FRC plasma. The resultant axial electroncurrent interacts with the radial magnetic field to produce an azimuthalbreaking force on the electrons, F_(θ)=−σV_(eθ)<|B_(r)|²>. For typicalconditions in the FRC system 10, the required applied magnetic dipole(or quadrupole) field inside the plasma needs to be only of order 0.001T to provide adequate electron breaking. The corresponding externalfield of about 0.015 T is small enough to not cause appreciable fastparticle losses or otherwise negatively impact confinement. In fact, theapplied magnetic dipole (or quadrupole) field contributes to suppressinstabilities. In combination with tangential neutral beam injection andaxial plasma injection, the saddle coils 460 provide an additional levelof control with regards to current maintenance and stability.

Mirror Plugs

The design of the pulsed coils 444 within the mirror plugs 440 permitsthe local generation of high magnetic fields (2 to 4 T) with modest(about 100 kJ) capacitive energy. For formation of magnetic fieldstypical of the present operation of the FRC system 10, all field lineswithin the formation volume are passing through the constrictions 442 atthe mirror plugs 440, as suggested by the magnetic field lines in FIG. 2and plasma wall contact does not occur. Furthermore, the mirror plugs440 in tandem with the quasi-dc divertor magnets 416 can be adjusted soto guide the field lines onto the divertor electrodes 910, or flare thefield lines in an end cusp configuration (not shown). The latterimproves stability and suppresses parallel electron thermal conduction.

The mirror plugs 440 by themselves also contribute to neutral gascontrol. The mirror plugs 440 permit a better utilization of thedeuterium gas puffed in to the quartz tubes during FRC formation, as gasback-streaming into the divertors 300 is significantly reduced by thesmall gas conductance of the plugs (a meager 500 L/s). Most of theresidual puffed gas inside the formation tubes 210 is quickly ionized.In addition, the high-density plasma flowing through the mirror plugs440 provides efficient neutral ionization hence an effective gasbarrier. As a result, most of the neutrals recycled in the divertors 300from the FRC edge layer 456 do not return to the confinement chamber100. In addition, the neutrals associated with the operation of theplasma guns 350 (as discussed below) will be mostly confined to thedivertors 300.

Finally, the mirror plugs 440 tend to improve the FRC edge layerconfinement. With mirror ratios (plug/confinement magnetic fields) inthe range 20 to 40, and with a 15 m length between the north and southmirror plugs 440, the edge layer particle confinement time τ_(∥)increases by up to an order of magnitude. Improving τ_(∥) readilyincreases the FRC particle confinement.

Assuming radial diffusive (D) particle loss from the separatrix volume453 balanced by axial loss (τ_(∥)) from the edge layer 456, one obtains(2πr_(s)L_(s))(Dn_(s)/δ)=(2πr_(s)L_(s)δ)(n_(s)/τ_(∥)), from which theseparatrix density gradient length can be rewritten as δ=(Dτ_(∥))^(1/2).Here r_(s), L_(s) and n_(s) are separatrix radius, separatrix length andseparatrix density, respectively. The FRC particle confinement time isτ_(N)=[πr_(s)²L_(s)<n>]/[(2πr_(s)L_(s))(Dn_(s)/δ)]=(<n>/n_(s))(τ_(⊥)τ_(∥))^(1/2),where τ_(⊥)=a²/D with a=r_(s)/4. Physically, improving τ_(∥) leads toincreased δ (reduced separatrix density gradient and drift parameter),and, therefore, reduced FRC particle loss. The overall improvement inFRC particle confinement is generally somewhat less than quadraticbecause n_(s) increases with τ_(∥).

A significant improvement in τ_(∥) also requires that the edge layer 456remains grossly stable (i.e., no n=1 flute, firehose, or other MHDinstability typical of open systems). Use of the plasma guns 350provides for this preferred edge stability. In this sense, the mirrorplugs 440 and plasma gun 350 form an effective edge control system.

Plasma Guns

The plasma guns 350 improve the stability of the FRC exhaust jets 454 byline-tying. The gun plasmas from the plasma guns 350 are generatedwithout azimuthal angular momentum, which proves useful in controllingFRC rotational instabilities. As such the guns 350 are an effectivemeans to control FRC stability without the need for the older quadrupolestabilization technique. As a result, the plasma guns 350 make itpossible to take advantage of the beneficial effects of fast particlesor access the advanced hybrid kinetic FRC regime as outlined in thisdisclosure. Therefore, the plasma guns 350 enable the FRC system 10 tobe operated with saddle coil currents just adequate for electronbreaking but below the threshold that would cause FRC instability and/orlead to dramatic fast particle diffusion.

As mentioned in the Mirror Plug discussion above, if τ_(II) can besignificantly improved, the supplied gun plasma would be comparable tothe edge layer particle loss rate (˜10²²/s). The lifetime of thegun-produced plasma in the FRC system 10 is in the millisecond range.Indeed, consider the gun plasma with density n_(e)˜10¹³ cm⁻³ and iontemperature of about 200 eV, confined between the end mirror plugs 440.The trap length L and mirror ratio R are about 15 m and 20,respectively. The ion mean free path due to Coulomb collisions isλ_(ii)˜6×10³ cm and, since λ_(ii)lnR/R<L, the ions are confined in thegas-dynamic regime. The plasma confinement time in this regime isτ_(gd)˜RL/2V_(s)˜2 ms, where V_(s) is the ion sound speed. Forcomparison, the classical ion confinement time for these plasmaparameters would be τ_(c)˜0.5τ_(ii)(lnR+(lnR)^(0.5))˜0.7 ms. Theanomalous transverse diffusion may, in principle, shorten the plasmaconfinement time. However, in the FRC system 10, if we assume the Bohmdiffusion rate, the estimated transverse confinement time for the gunplasma is τ_(⊥)>τ_(gd)˜2 ms. Hence, the guns would provide significantrefueling of the FRC edge layer 456, and an improved overall FRCparticle confinement.

Furthermore, the gun plasma streams can be turned on in about 150 to 200microseconds, which permits use in FRC start-up, translation, andmerging into the confinement chamber 100. If turned on around t˜0 (FRCmain bank initiation), the gun plasmas help to sustain the presentdynamically formed and merged FRC 450. The combined particle inventoriesfrom the formation FRCs and from the guns is adequate for neutral beamcapture, plasma heating, and long sustainment. If turned on at tin therange −1 to 0 ms, the gun plasmas can fill the quartz tubes 210 withplasma or ionize the gas puffed into the quartz tubes, thus permittingFRC formation with reduced or even perhaps zero puffed gas. The lattermay require sufficiently cold formation plasma to permit fast diffusionof the reversed bias magnetic field. If turned on at t<−2 ms, the plasmastreams could fill the about 1 to 3 m³ field line volume of theformation and confinement regions of the formation sections 200 andconfinement chamber 100 with a target plasma density of a few 10¹³ cm⁻³,sufficient to allow neutral beam build-up prior to FRC arrival. Theformation FRCs could then be formed and translated into the resultingconfinement vessel plasma. In this way the plasma guns 350 enable a widevariety of operating conditions and parameter regimes.

Electrical Biasing

Control of the radial electric field profile in the edge layer 456 isbeneficial in various ways to FRC stability and confinement. By virtueof the innovative biasing components deployed in the FRC system 10 it ispossible to apply a variety of deliberate distributions of electricpotentials to a group of open flux surfaces throughout the machine fromareas well outside the central confinement region in the confinementchamber 100. In this way radial electric fields can be generated acrossthe edge layer 456 just outside of the FRC 450. These radial electricfields then modify the azimuthal rotation of the edge layer 456 andeffect its confinement via ExB velocity shear. Any differential rotationbetween the edge layer 456 and the FRC core 453 can then be transmittedto the inside of the FRC plasma by shear. As a result, controlling theedge layer 456 directly impacts the FRC core 453. Furthermore, since thefree energy in the plasma rotation can also be responsible forinstabilities, this technique provides a direct means to control theonset and growth of instabilities. In the FRC system 10, appropriateedge biasing provides an effective control of open field line transportand rotation as well as FRC core rotation. The location and shape of thevarious provided electrodes 900, 905, 910 and 920 allows for control ofdifferent groups of flux surfaces 455 and at different and independentpotentials. In this way a wide array of different electric fieldconfigurations and strengths can be realized, each with differentcharacteristic impact on plasma performance.

A key advantage of all these innovative biasing techniques is the factthat core and edge plasma behavior can be effected from well outside theFRC plasma, i.e. there is no need to bring any physical components intouch with the central hot plasma (which would have severe implicationsfor energy, flux and particle losses). This has a major beneficialimpact on performance and all potential applications of the HPF concept.

Experimental Data—HPF Operation

Injection of fast particles via beams from the neutral beam guns 600plays an important role in enabling the HPF regime. FIGS. 16A, 16B, 16C,and 16D illustrate this fact. Depicted is a set of curves showing howthe FRC lifetime correlates with the length of the beam pulses. Allother operating conditions are held constant for all dischargescomprising this study. The data is averaged over many shots and,therefore, represents typical behavior. It is clearly evident thatlonger beam duration produces longer lived FRCs. Looking at thisevidence as well as other diagnostics during this study, it demonstratesthat beams increase stability and reduce losses. The correlation betweenbeam pulse length and FRC lifetime is not perfect as beam trappingbecomes inefficient below a certain plasma size, i.e., as the FRC 450shrinks in physical size not all of the injected beams are interceptedand trapped. Shrinkage of the FRC is primarily due to the fact that netenergy loss (˜4 MW about midway through the discharge) from the FRCplasma during the discharge is somewhat larger than the total power fedinto the FRC via the neutral beams (˜2.5 MW) for the particularexperimental setup. Locating the beams at a location closer to themid-plane of the vessel 100 would tend to reduce these losses and extendFRC lifetime.

FIGS. 17A, 17B, 17C, and 17D illustrate the effects of differentcomponents to achieve the HPF regime. It shows a family of typicalcurves depicting the lifetime of the FRC 450 as a function of time. Inall cases a constant, modest amount of beam power (about 2.5 MW) isinjected for the full duration of each discharge. Each curve isrepresentative of a different combination of components. For example,operating the FRC system 10 without any mirror plugs 440, plasma guns350 or gettering from the gettering systems 800 results in rapid onsetof rotational instability and loss of the FRC topology. Adding only themirror plugs 440 delays the onset of instabilities and increasesconfinement. Utilizing the combination of mirror plugs 440 and a plasmagun 350 further reduces instabilities and increases FRC lifetime.Finally adding gettering (Ti in this case) on top of the gun 350 andplugs 440 yields the best results—the resultant FRC is free ofinstabilities and exhibits the longest lifetime. It is clear from thisexperimental demonstration that the full combination of componentsproduces the best effect and provides the beams with the best targetconditions.

As shown in FIG. 1, the newly discovered HPF regime exhibitsdramatically improved transport behavior. FIG. 1 illustrates the changein particle confinement time in the FRC system 10 between theconventionally regime and the HPF regime. As can be seen, it hasimproved by well over a factor of 5 in the HPF regime. In addition, FIG.1 details the particle confinement time in the FRC system 10 relative tothe particle confinement time in prior conventional FRC experiments.With regards to these other machines, the HPF regime of the FRC system10 has improved confinement by a factor of between 5 and close to 20.Finally and most importantly, the nature of the confinement scaling ofthe FRC system 10 in the HPF regime is dramatically different from allprior measurements. Before the establishment of the HPF regime in theFRC system 10, various empirical scaling laws were derived from data topredict confinement times in prior FRC experiments. All those scalingrules depend mostly on the ratio R²/ρ_(i), where R is the radius of themagnetic field null (a loose measure of the physical scale of themachine) and ρ_(i) is the ion larmor radius evaluated in the externallyapplied field (a loose measure of the applied magnetic field). It isclear from FIG. 1 that long confinement in conventional FRCs is onlypossible at large machine size and/or high magnetic field. Operating theFRC system 10 in the conventional FRC regime CR tends to follow thosescaling rules, as indicated in FIG. 1. However, the HPF regime is vastlysuperior and shows that much better confinement is attainable withoutlarge machine size or high magnetic fields. More importantly, it is alsoclear from FIG. 1 that the HPF regime results in improved confinementtime with reduced plasma size as compared to the CR regime. Similartrends are also visible for flux and energy confinement times, asdescribed below, which have increased by over a factor of 3-8 in the FRCsystem 10 as well. The breakthrough of the HPF regime, therefore,enables the use of modest beam power, lower magnetic fields and smallersize to sustain and maintain FRC equilibria in the FRC system 10 andfuture higher energy machines. Hand-in-hand with these improvementscomes lower operating and construction costs as well as reducedengineering complexity.

For further comparison, FIGS. 18A, 18B, 18C, and 18D show data from arepresentative HPF regime discharge in the FRC system 10 as a functionof time. FIG. 18A depicts the excluded flux radius at the mid-plane. Forthese longer timescales the conducting steel wall is no longer as good aflux conserver and the magnetic probes internal to the wall areaugmented with probes outside the wall to properly account for magneticflux diffusion through the steel. Compared to typical performance in theconventional regime CR, as shown in FIGS. 13A, 13B, 13C, and 13D, theHPF regime operating mode exhibits over 400% longer lifetime.

A representative cord of the line integrated density trace is shown inFIG. 18B with its Abel inverted complement, the density contours, inFIG. 18C. Compared to the conventional FRC regime CR, as shown in FIGS.13A, 13B, 13C, and 13D, the plasma is more quiescent throughout thepulse, indicative of very stable operation. The peak density is alsoslightly lower in HPF shots—this is a consequence of the hotter totalplasma temperature (up to a factor of 2) as shown in FIG. 18D.

For the respective discharge illustrated in FIGS. 18A, 18B, 18C, and18D, the energy, particle and flux confinement times are 0.5 ms, 1 msand 1 ms, respectively. At a reference time of 1 ms into the discharge,the stored plasma energy is 2 kJ while the losses are about 4 MW, makingthis target very suitable for neutral beam sustainment.

FIG. 19 summarizes all advantages of the HPF regime in the form of anewly established experimental HPF flux confinement scaling. As can beseen in FIG. 19, based on measurements taken before and after t=0.5 ms,i.e., t≤0.5 ms and t>0.5 ms, the flux confinement (and similarly,particle confinement and energy confinement) scales with roughly thesquare of the electron Temperature (T_(e)) for a given separatrix radius(r_(s)). This strong scaling with a positive power of T_(e) (and not anegative power) is completely opposite to that exhibited by conventionaltokomaks, where confinement is typically inversely proportional to somepower of the electron temperature. The manifestation of this scaling isa direct consequence of the HPF state and the large orbit (i.e. orbitson the scale of the FRC topology and/or at least the characteristicmagnetic field gradient length scale) ion population. Fundamentally,this new scaling substantially favors high operating temperatures andenables relatively modest sized reactors.

With the advantages the HPF regime presents, FRC sustainment or steadystate driven by neutral beams and using appropriate pellet injection isachievable, meaning global plasma parameters such as plasma thermalenergy, total particle numbers, plasma radius and length as well asmagnetic flux are sustainable at reasonable levels without substantialdecay. For comparison, FIG. 20 shows data in plot A from arepresentative HPF regime discharge in the FRC system 10 as a functionof time and in plot B for a projected representative HPF regimedischarge in the FRC system 10 as a function of time where the FRC 450is sustained without decay through the duration of the neutral beampulse. For plot A, neutral beams with total power in the range of about2.5-2.9 MW were injected into the FRC 450 for an active beam pulselength of about 6 ms. The plasma diamagnetic lifetime depicted in plot Awas about 5.2 ms. More recent data shows a plasma diamagnetic lifetimeof about 7.2 ms is achievable with an active beam pulse length of about7 ms.

As noted above with regard to FIGS. 16A, 16B, 16C, and 16D, thecorrelation between beam pulse length and FRC lifetime is not perfect asbeam trapping becomes inefficient below a certain plasma size, i.e., asthe FRC 450 shrinks in physical size not all of the injected beams areintercepted and trapped. Shrinkage or decay of the FRC is primarily dueto the fact that net energy loss (−4 MW about midway through thedischarge) from the FRC plasma during the discharge is somewhat largerthan the total power fed into the FRC via the neutral beams (−2.5 MW)for the particular experimental setup. As noted with regard to FIG. 3C,angled beam injection from the neutral beam guns 600 towards themid-plane improves beam-plasma coupling, even as the FRC plasma shrinksor otherwise axially contracts during the injection period. In addition,appropriate pellet fueling will maintain the requisite plasma density.

Plot B is the result of simulations run using an active beam pulselength of about 6 ms and total beam power from the neutral beam guns 600of slightly more than about 10 MW, where neutral beams shall inject H(or D) neutrals with particle energy of about 15 keV. The equivalentcurrent injected by each of the beams is about 110 A. For plot B, thebeam injection angle to the device axis was about 20°, target radius0.19 m. Injection angle can be changed within the range 15°-25°. Thebeams are to be injected in the co-current direction azimuthally. Thenet side force as well as net axial force from the neutral beam momentuminjection shall be minimized. As with plot A, fast (H) neutrals areinjected from the neutral beam injectors 600 from the moment the northand south formation FRCs merge in the confinement chamber 100 into oneFRC 450.

The simulations that where the foundation for plot B usemulti-dimensional hall-MHD solvers for the background plasma andequilibrium, fully kinetic Monte-Carlo based solvers for the energeticbeam components and all scattering processes, as well as a host ofcoupled transport equations for all plasma species to model interactiveloss processes. The transport components are empirically calibrated andextensively benchmarked against an experimental database.

As shown by plot B, the steady state diamagnetic lifetime of the FRC 450will be the length of the beam pulse. However, it is important to notethat the key correlation plot B shows is that when the beams are turnedoff the plasma or FRC begins to decay at that time, but not before. Thedecay will be similar to that which is observed in discharges which arenot beam-assisted—probably on order of 1 ms beyond the beam turn offtime—and is simply a reflection of the characteristic decay time of theplasma driven by the intrinsic loss processes.

Plasma Stability and Axial Position Control

Turning now to the systems and methods that facilitate stability of anFRC plasma in both radial and axial directions and axial positioncontrol of an FRC plasma along the symmetry axis of an FRC plasmaconfinement chamber, FIG. 24 shows a simplified scheme to illustrate anexample embodiment of an axial position control mechanism 510. Arotating FRC plasma 520 shown within a confinement chamber 100 has aplasma current 522 and an axial displacement direction 524. Anequilibrium field (not shown) is produced within the chamber 100 bysymmetric current components such as, e.g., the quasi-dc coils 412 (seeFIGS. 2 and 3A). The equilibrium field does not produce a net force inthe axial displace direction 524, but can be tuned to produce either atransversally/radially or axially stable plasma. For the purposes of theembodiment presented herein, the equilibrium field is tuned to produce atransversally/radially stable FRC plasma 520. As noted above, thisresults in axial instability and, thus, axial displacement of the FRCplasma 520 in an axial displacement direction 524. As the FRC plasma 520moves axially it induces current 514 and 516 that are antisymmetric,i.e., in counter directions in the walls of the confinement chamber 100on each side of the mid-plane of the confinement chamber 100. The FRCplasma 520 will induce these type of current components in both thevessel and also in the external coils. This antisymmetric currentcomponents 514 and 516 produce a radial field which interacts with thetoroidal plasma current 522 to produce a force that opposes the movementof the FRC plasm 520, and the result of this force is that it slows downplasma axial displacements. These currents 514 and 516 graduallydissipate with time, due to the resistivity of the confinement chamber100.

Radial field coils 530 and 531 disposed about the confinement chamber100 on each side of the mid-plane provide additional radial fieldcomponents that are due to the currents 532 and 534 induced in counterdirections in the coils 530 and 531. The radial field coils 530 and 531may comprise a set of axisymmetric coils that may be positioned internalor external to the containment vessel 100. The radial coils 530 and 531are shown to be positioned external to the containment vessel 100similar to the quasi-dc coils 412 (see, FIGS. 2 and 3A). Each of thecoils 530 and 531, or sets of coils, may carry a different current thanthe coils on the opposite side of the mid-plane, but the currents areantisymmetric with respect to the mid-plane of the containment vessel100 and produce a magnetic field structure with B_(z)≠0, B_(r)=0 alongthe midplane. The radial field coils 530 and 531 create a supplementalradial field component that interacts with the toroidal plasma current522 to produce an axial force. The axial force in turn moves the plasmaback towards the mid-plane of the confinement chamber 100.

The control mechanism 510 includes a control system configured to act onthe radial field coil current in order to expeditiously restore theplasma position towards the mid-plane while minimizing overshootingand/or oscillations around the machine mid-plane. The control systemincludes a processor operably coupled to the radial field coils 530 and531, the quasi-dc coils 412, their respective power supplies, and othercomponents such as, e.g., magnetic sensors, providing plasma position,plasma velocity, and active coil current measurements. The processor maybe configured to perform the computations and analyses described in thepresent application and may include or be communicatively coupled to oneor more memories including non-transitory computer readable medium. Itmay include a processor-based or microprocessor-based system includingsystems using microcontrollers, reduced instruction set computers(RISC), application specific integrated circuits (ASICs), logiccircuits, and any other circuit or processor capable of executing thefunctions described herein. The above examples are exemplary only, andare thus not intended to limit in any way the definition and/or meaningof the term “processor” or “computer.”

Functions of the processor may be implemented using either softwareroutines, hardware components, or combinations thereof. The hardwarecomponents may be implemented using a variety of technologies,including, for example, integrated circuits or discrete electroniccomponents. The processor unit typically includes a readable/writeablememory storage device and typically also includes the hardware and/orsoftware to write to and/or read the memory storage device.

The processor may include a computing device, an input device, a displayunit and an interface, for example, for accessing the Internet. Thecomputer or processor may include a microprocessor. The microprocessormay be connected to a communication bus. The computer or processor mayalso include a memory. The memory may include Random Access Memory (RAM)and Read Only Memory (ROM). The computer or processor may also include astorage device, which may be a hard disk drive or a removable storagedrive such as a floppy disk drive, optical disk drive, and the like. Thestorage device may also be other similar means for loading computerprograms or other instructions into the computer or processor.

The processor executes a set of instructions that are stored in one ormore storage elements, in order to process input data. The storageelements may also store data or other information as desired or needed.The storage element may be in the form of an information source or aphysical memory element within a processing machine.

The problem of controlling the position of an axially stable or unstableFRC configuration using the radial field coil actuators is solved usinga branch of non-linear control theory known as sliding mode control. Alinear function of system states (the sliding surface) acts as the errorsignal with the desired asymptotically stable (sliding) behavior. Thesliding surface is designed using Liapunov theory to exhibit asymptoticstability in a broad range of FRC dynamic parameters. The proposedcontrol scheme can then be used for both axially stable and unstableplasmas without the need to re-tune the parameters used in the slidingsurface. This property is advantageous because, as mentioned before, theequilibrium may have to transit between axially stable and axiallyunstable equilibria on different phases of the FRC discharge.

The configuration of the control scheme 500 is shown in FIG. 25. The lowpass filter restricts the switching frequencies within the desiredcontrol bandwidth. A digital control loop requiring sampling and signaltransmission with one sample delay is assumed. The error signal (thesliding surface) is a linear combination of coil current, plasmaposition and plasma velocity. Plasma position and velocity of the plasmaare obtained from external magnetic measurements. Currents in the activecoil systems can be measured by standard methods.

Coil currents and plasma position are required to implement the positioncontrol. Plasma velocity is required to improve performance but isoptional. A non-linear function of this error signal (relay control law)generates discrete voltage levels for every pair of power suppliesconnected to mid-plane symmetric coils. Midplane symmetric coils arefeed with relay voltages of same intensity but opposite sign. Thiscreates a radial field component to restore the plasma position towardsthe mid-plane.

To demonstrate the feasibility of the control scheme, a rigid plasmamodel is used to simulate the plasma dynamics. The model utilizes amagnet geometry. Plasma current distribution corresponds to axiallyunstable equilibria with a growth time of 2 ms when only plasma andvessel are considered. The power supplies are assumed to work withdiscrete voltage levels, typically in 800 V steps.

FIG. 26 shows several plasma control simulations that highlight therelationship between applied voltages to the coils, and the plasmaposition settling times, along with the required coil peak current andramp rates to bring back to the mid-plane a plasma that was displacedaxially by 20 cm. These sliding mode axial position control simulationexamples are run at 0.3 T using four pairs of external trim coils. Fourcases are shown corresponding with power supplies with discrete voltagelevels in steps of 200 V (solid square), 400V (solid circle), 800 V(solid triangle) and 1600 V (hollow square). For all four cases thecontrol bandwidth is 16 kHz and sampling frequency is 32 kHz. The plasmaposition (top figure), current in the outermost coil pair (middle) andcoil current ramp-rate (bottom) are shown. Plasma displacement isallowed to grow unstable until it reaches 20 cm. At this point thefeedback control is applied.

Simulation results indicate that:

-   -   1. To bring the plasma back to the mid-plane within 5 ms (solid        square traces), coil ramp-up rate of 0.5 MA/s suffices,        requiring a 200 V power supply.    -   2. To bring the plasma back to the mid-plane within 2.3 ms        (solid circle traces), coil ramp-up rate of 1 MA/s suffices,        requiring a 400 V power supply.    -   3. To bring the plasma back to the mid-plane within 1.3 ms        (solid triangle traces), coil ramp-up rate of 2 MA/s suffices,        requiring an 800 V power supply.    -   4. To bring the plasma back to the mid-plane within 1.0 ms        (hollow square traces), coil ramp-up rate of 4 MA/s suffices,        requiring a 1600 V power supply.

The peak currents for all the trim coils for the third case studiedabove (the 2 MA/s ramp rate case) are also shown in FIG. 27 as functionof trim coil position. The sliding mode axial position controlsimulation examples are run at 0.3 T using four pairs of external trimcoils using a power supply with three levels (+800V, 0, −800V), acontrol bandwidth of 16 kHz and a sampling rate of 32 kHz. To bring theplasma back to the mid-plane within 1.3 ms, coil ramp-up rate of 2 MA/sis required. The peak current required in all coil pair is less than 1.5kA. The actual switching frequency required (about 2 kHz) is well belowthe control system bandwidth

The control system can also be implemented a target surface which isfunction of coil current and plasma velocity alone, without plasmaposition. In this case the axial position control loop provides onlystabilization of the axial dynamics, but not control. This means thatthe plasma is in a metastable situation and can drift slowly along itsaxis. The position control is then provided using an additional feedbackloop that controls the plasma gaps between plasma separatrix and vessel,hence it performs plasma shape and position control simultaneously.

Another plasma confinement device where similar control systems are usedis the tokamak. To maintain plasma confinement, the plasma current in atokamak must be kept between a lower and an upper limit that are roughlyproportional to plasma density and toroidal field, respectively. Tooperate at high plasma density plasma current must be increased. At thesame time the poloidal field must be kept as low as possible so the qsafety factor is above q=2. This is achieved by elongating the plasmaalong the machine axis direction, allowing to fit large plasma current(and hence allow high plasma density) without increasing the boundarymagnetic field above its safety limits. These elongated plasmas areunstable along the machine axis direction (known in tokamak jargon asthe vertical direction), and also require plasma stabilizationmechanisms. Vertical plasma position control in tokamaks is alsorestored using a set of radial field coils, so it strongly resembles theRFC position control problem. However the reasons to requirestabilization in a tokamak and an FRC are different. In a tokamak plasmavertical instability is a penalty to be paid to operate at large plasmacurrent, which requires plasma elongation to operate with high toroidalfield. In the case of the FRC, plasma instability is a penalty to bepaid to obtain transverse stability. Tokamaks have toroidal field thatstabilizes the configuration, so they don't need transversestabilization.

The example embodiments provided herein have been described in U.S.Provisional Patent Application No. 62/255,258 and U.S. ProvisionalPatent Application No. 62/309,344, which applications are incorporatedby reference.

The example embodiments provided herein, however, are merely intended asillustrative examples and not to be limiting in any way.

All features, elements, components, functions, and steps described withrespect to any embodiment provided herein are intended to be freelycombinable and substitutable with those from any other embodiment. If acertain feature, element, component, function, or step is described withrespect to only one embodiment, then it should be understood that thatfeature, element, component, function, or step can be used with everyother embodiment described herein unless explicitly stated otherwise.This paragraph therefore serves as antecedent basis and written supportfor the introduction of claims, at any time, that combine features,elements, components, functions, and steps from different embodiments,or that substitute features, elements, components, functions, and stepsfrom one embodiment with those of another, even if the followingdescription does not explicitly state, in a particular instance, thatsuch combinations or substitutions are possible. Express recitation ofevery possible combination and substitution is overly burdensome,especially given that the permissibility of each and every suchcombination and substitution will be readily recognized by those ofordinary skill in the art upon reading this description.

In many instances entities are described herein as being coupled toother entities. It should be understood that the terms “coupled” and“connected” (or any of their forms) are used interchangeably herein and,in both cases, are generic to the direct coupling of two entities(without any non-negligible (e.g., parasitic) intervening entities) andthe indirect coupling of two entities (with one or more non-negligibleintervening entities). Where entities are shown as being directlycoupled together, or described as coupled together without descriptionof any intervening entity, it should be understood that those entitiescan be indirectly coupled together as well unless the context clearlydictates otherwise.

While the embodiments are susceptible to various modifications andalternative forms, specific examples thereof have been shown in thedrawings and are herein described in detail. It should be understood,however, that these embodiments are not to be limited to the particularform disclosed, but to the contrary, these embodiments are to cover allmodifications, equivalents, and alternatives falling within the spiritof the disclosure. Furthermore, any features, functions, steps, orelements of the embodiments may be recited in or added to the claims, aswell as negative limitations that define the inventive scope of theclaims by features, functions, steps, or elements that are not withinthat scope.

What is claimed is:
 1. A method for stabilizing a field reversedconfiguration (FRC) plasma comprising the steps of: forming an FRCplasma positioned along a longitudinal axis of a confinement chamberadjacent a mid-plane of the confinement chamber by forming an FRCmagnetic field about a rotating plasma in the confinement chamber;stabilizing the FRC plasma in a radial direction normal to thelongitudinal axis to position the FRC plasma axisymmetric about thelongitudinal axis by adjusting an applied magnetic field to induceradial stability and axial instability in the FRC plasma; andstabilizing the FRC plasma in an axial direction along the longitudinalaxis by adjusting first and second radial magnetic fields, wherein thefirst and second radial magnetic fields interact with the FRC magneticfield to axially move the FRC plasma to position the FRC plasmaaxisymmetric about the mid-plane.
 2. The method of claim 1 furthercomprising the step of generating an applied magnetic field within thechamber with quasi-dc coils encircling the confinement chamber andextending axially along the confinement chamber.
 3. The method of claim1 further comprising the step of axially injecting plasma into the FRCplasma from axially mounted plasma guns.
 4. The method of claim 1wherein the first and second radial magnetic fields are antisymmetricabout the mid-plane.
 5. The method of claim 4 wherein the first andsecond radial magnetic fields are generated due to currents induced incounter directions in first and second radial coils positioned about theconfinement chamber.
 6. The method of claim 1 wherein the step ofstabilizing the FRC plasma includes monitoring the position of the FRCplasma.
 7. The method of claim 6 wherein the step of monitoring theposition of the FRC plasma includes monitoring magnetic measurementsassociated with the FRC plasma.
 8. The method of claim 6 furthercomprising the step of measuring current in the first and second radialcoils.
 9. The method of claim 8 further comprising the step ofmonitoring the velocity of the FRC plasma.
 10. The method of claim 1further comprising maintaining one or more of plasma thermal energy,plasma particle count, plasma radius, plasma length and magnetic flux ofthe FRC plasma at or about a constant value without decay by injectingbeams of fast neutral atoms from neutral beam injectors into the FRCplasma at an angle towards the mid-plane of the confinement chamber andinjecting a compact toroid plasma into the FRC plasma.
 11. The method ofclaim 10 further comprising the step of generating a mirror magneticfield within opposing ends of the confinement chamber with quasi-dcmirror coils extending about the opposing ends of the confinementchamber.
 12. The method of claim 1 wherein the step of the forming theFRC plasma includes forming a formation FRC plasma in a first formationsection coupled to an end of the confinement chamber and acceleratingthe formation FRC plasma towards the mid-plane of the confinementchamber to form the FRC plasma.
 13. The method of claim 12 wherein thestep of the forming the FRC plasma includes forming a second formationFRC plasma in a second formation section coupled to a second end of theconfinement chamber and accelerating the second formation FRC plasmatowards the mid-plane of the confinement chamber where the two formationFRC plasmas merge to form the FRC plasma.
 14. The method of claim 12wherein the step of forming the FRC plasma includes one of forming aformation FRC plasma while accelerating the formation FRC plasma towardsthe mid-plane of the confinement chamber and forming a formation FRCplasma then accelerating the formation FRC plasma towards the mid-planeof the confinement chamber.
 15. The method of claim 13 furthercomprising the step of guiding magnetic flux surfaces of the FRCmagnetic field into diverters coupled to the ends of the first andsecond formation sections.
 16. The method of claim 1 further comprisingthe step of conditioning the internal surfaces of the chamber, formationsections, and diverters with a gettering system.
 17. The method of claim16 wherein the gettering system includes one of a Titanium depositionsystem and a Lithium deposition system.
 18. The method of claim 1further comprising the step of controlling a radial electric fieldprofile in an edge layer of the FRC plasma.
 19. The method of claim 18wherein the step of controlling the radial electric field profile in theedge layer of the FRC plasma includes applying a distribution ofelectric potential to a group of open flux surfaces of the FRC plasmawith biasing electrodes.